\documentclass[10pt,a4paper]{article} 

\usepackage{ctex} % 中文支持
\usepackage[top=2.5cm, bottom=2.5cm, left=2.5cm, right=2.5cm]{geometry} % 页边距
\usepackage{amsmath, amssymb} % 数学公式与符号
\usepackage{graphicx}
\usepackage{pythonhighlight}
\usepackage{url} 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{titling}
\setlength{\droptitle}{-2cm} % 标题上移

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 使表格美观
\usepackage{array}
\newcolumntype{M}[1]{>{\centering\arraybackslash}m{#1}}
\setlength\extrarowheight{3pt}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%文档的题目、作者与日期
\author{五六七 }
\title{使用数据包络分析的可持续发展评价 }

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}

\maketitle

\begin{abstract}
利用数据包络方法对天津市的可持续发展进行评价。
\end{abstract}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\setcounter{tocdepth}{2}
%\renewcommand\contentsname{目录}
%
%\renewcommand {\baselinestretch} {1.3}\normalsize 
%\tableofcontents 
%\renewcommand {\baselinestretch} {1.0}\normalsize


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{问题描述}
数据包络分析是评价具有多指标输入和多指标输出系统的一种方法。
天津市的一些经济指标在1990-1999年的数据如表所示。
请使用数据包络分析对其可持续发展进行评价。

\begin{table}[ht!]\centering
\caption{变量名称与含义} \vspace{0.2cm}
\begin{tabular}{|p{2cm}|p{6cm}|p{2cm}|}\hline
变量名 & 含义 & 单位  \\ \hline 
$x_1$ & 政府财政收入占GDP的比重 & \% \\ \hline 
$x_2$ & 环保投资占GDP的比重 & \% \\ \hline 
$x_3$ & 每千人中的科技人员人数 & 人 \\ \hline 
$x_4$ & 人均 GDP & 元 \\ \hline 
$x_5$ & 城市环境质量指数 &  \\ \hline  
\end{tabular}
\end{table}

\begin{table}[ht!]\centering
\caption{各决策单元输入输出指标值} \vspace{0.2cm}
\begin{tabular}{|M{1.5cm}|M{1.5cm}|M{1.5cm}|M{1.5cm}|M{1.5cm}|M{1.5cm}|M{1.5cm}|}\hline 
序号 & 决策单元 & $x_1$ & $x_2$ & $x_3$ & $x_4$ & $x_5$   \\ \hline 
1	&	1990	&	14.4	&	0.65	&	31.3	&	3621	&	0		\\ \hline 
2	&	1991	&	16.9	&	0.72	&	32.2	&	3943	&	0.09		\\ \hline 
3	&	1992	&	15.53	&	0.72	&	31.87	&	4086.67	&	0.07		\\ \hline 
4	&	1993	&	15.4	&	0.76	&	32.23	&	4904.67	&	0.13		\\ \hline 
5	&	1994	&	14.17	&	0.76	&	32.4	&	6311.67	&	0.37		\\ \hline 
6	&	1995	&	13.33	&	0.69	&	30.77	&	8173.33	&	0.59		\\ \hline 
7	&	1996	&	12.83	&	0.61	&	29.23	&	10236	&	0.51		\\ \hline 
8	&	1997	&	13	&	0.63	&	28.2	&	12094.33	&	0.44		\\ \hline 
9	&	1998	&	13.4	&	0.75	&	28.8	&	13603.33	&	0.58		\\ \hline 
10	&	1999	&	14	&	0.84	&	29.1	&	14841	&	1		\\ \hline 
\end{tabular}
\end{table}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{建立模型}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{编程计算}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{检验模型}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{回答问题}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{参考文献 }
\begin{thebibliography}{99}

%\bibitem{dingtongren} 丁同仁、李承治，常微分方程教程，高等教育出版社，2022年3月第三版。
\bibitem{sishoukui-2} 司守奎,孙玺菁. \emph{Python数学建模算法与应用}, 国防工业出版社. 2022年1月第1版. 
%\bibitem{hexiaoqun-ara} 何晓群. \emph{应用回归分析(R语言版)}. 电子工业出版社. 2017年7月第1版. 
%\bibitem{dalgaard} Peter Dalgaard 著, 郝智恒等译. \emph{R语言统计入门}. 人民邮电出版社. 2014年6月第1版. 


\end{thebibliography}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





